Partition functions, adiabatic exponent and their role in the analysis of spectroscopic Doppler shift in determining the Mach number and temperature of a hypersonic plasma jet

Theoretical estimates of the thermodynamic properties of the argon plasma jet play an important role in the analysis and interpretation of the experimental data on the testing and commissioning of the STG1 plasma gun. In particular, the analysis of spectroscopic and laser interferometric data are sensitive to the estimates of the ratio of specific heats (the adiabatic exponent g) and the temperature of the plasma jets. The method of partition functions provides the most systematic method of computing the thermodynamic properties of systems. Whereas there is a large amount of literature available giving the partition functions of argon [e.g. 1–3], it is found that the available information is not usually presented in the most convenient format, nor in the required density and temperature range of interest to the present phase of our project in developing the STG1 plasma gun. For the purpose of fast dissemination, we summarize in this Tech Note the results of our calculations of these critical thermodynamic properties. The computation is developed using a simplified approach on ionization and partition functions based on the hydrogen-like ion model as described in Zel’dovich and Raizer [4]. The results show that the adiabatic exponent g and the corresponding degree of ionization of an argon plasma go through very sharp transitions in a narrow temperature window in the temperature range between 0.5 eV and 1.5 eV for particle density in the range from $10^{21} \mathrm{~m}^{-3}$ to $10^{24} \mathrm{~m}^{-3}$. As the properties of the plasma jets launched by the STG1 plasma gun fall right in these regimes, this circumstance provides exciting opportunities for the spectroscopic and laser interferometric measurements. The theoretical development and results are applied to the analysis of spectroscopy data relating to the Doppler shift measured in the determination of the Mach number of a hypersonic plasma jet.